Semiclassical treatment of quadrupole boson hamiltonians: new results for small and large amplitude regimes

Abstract

Abstract A fourth order quadrupole boson hamiltonian is semiclassically treated through a time dependent variational principle (TDVP), the variational states being of coherent type for boson operators b 20 + , ( 1 2 )(b 22 + + b 2−2 + ) . The static ground state is studied as a function of the parameters involved in the model hamiltonian. Linearizing the classical equations of motion one obtains the RPA approach for the many boson correlations. There are two RPA roots which describe the beta and gamma vibrations, respectively. Several quantization procedures for both small and large amplitude regimes are discussed. The quantized hamiltonians are compared with some others which were previously obtained by using different methods. A special attention is paid to the quantal states associated to some of the peaks appearing in the Fourier spectrum of the classical action density. Some of the quantal states exhibit a pronounced anharmonic structure. Therefore the procedure may be used for a unified description of small and large amplitude regimes.